9 papers
Variational convexity: new characterizations, calculus rules, and applications
Radu Ioan Bot, Ziyuan Wang
Introduced by R.T. Rockafellar in 2019, variational convexity is a generalized notion of convexity under which stationary points of nonconvex optimization problems can still be gua…
The Iterates of Nesterov's Accelerated Algorithm Converge in The Critical Regimes
Radu Ioan Bot, Jalal Fadili, Dang-Khoa Nguyen
In this paper, we prove that the iterates of the accelerated Nesterov's algorithm in the critical regime do converge in the weak topology to a global minimizer of an -smooth fun…
Fast Reflected Forward-Backward algorithm: achieving fast convergence rates for convex optimization with linear cone constraints
Radu Ioan Bot, Dang-Khoa Nguyen, Chunxiang Zong
In this paper, we derive a Fast Reflected Forward-Backward (Fast RFB) algorithm to solve the problem of finding a zero of the sum of a maximally monotone operator and a monotone an…
Long-Time Analysis of Stochastic Heavy Ball Dynamics for Convex Optimization and Monotone Equations
Radu Ioan Bot, Chiara Schindler
In a separable real Hilbert space, we study the problem of minimizing a convex function with Lipschitz continuous gradient in the presence of noisy evaluations. To this end, we ass…
Inertial dynamics with vanishing Tikhonov regularization for multiobjective optimization
Radu Ioan Bot, Konstantin Sonntag
In this paper, we introduce, in a Hilbert space setting, a second order dynamical system with asymptotically vanishing damping and vanishing Tikhonov regularization that approaches…
A full splitting algorithm for structured difference-of-convex programs
Radu Ioan Bot, Rossen Nenov, Min Tao
In this paper, we study a class of nonconvex and nonsmooth structured difference-of-convex (DC) programs, which contain in the convex part the sum of a nonsmooth linearly composed…